Boys to girls

The ratio of boys to girls in a party is 3:5 . If 6 more boys arrived and 4 girls left the party, the ratio of boys to girls would be 5:6 . How many are in the party originally?

Result

t =  64

Solution:

 t=a+b a=3/5⋅ b (a+6)=5/6⋅ (b−4)  a+b−t=0 5a−3b=0 6a−5b=−56  a=24 b=40 t=64 =64 \ \\ t=a+b \ \\ a=3/5 \cdot \ b \ \\ (a+6)=5/6 \cdot \ (b-4) \ \\ \ \\ a+b-t=0 \ \\ 5a-3b=0 \ \\ 6a-5b=-56 \ \\ \ \\ a=24 \ \\ b=40 \ \\ t=64 \ \\ =64

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